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LowTFMuonium¶
Description¶
A relaxation function for a pair of transver field triplet muonium frequencies.
\[A(t)=\frac{A_0}{4}\{(1+\delta)a_{12}\cos(\omega_{12}+\phi)+ (1-\delta)a_{23}\cos(\omega_{23}+\phi)\}\]
and,
\[\delta= \frac{\chi}{\sqrt{1+\chi^2}},\]
\[\chi = (g_\mu+g_e)\frac{B}{A},\]
\[d = \frac{(g_e-g_\mu)}{g_e+g_\mu},\]
\[E_1=\frac{A}{4}(1+2d\chi),\]
\[E_2=\frac{A}{4}(-1+2\sqrt{1+\chi^2}),\]
\[E_3=\frac{A}{4}(1-2d\chi),\]
\[\omega_{ij}= 2 \pi (E_i - E_j),\]
\[a_{ij}=\frac{1}{(1+(\omega_{ij}/(2\pi f_\text{cut}))^2)},\]
where,
\(A_0\) is the amplitude,
A (MHz) is the isotropic hyperfine coupling constant,
\(\phi\) (rad) is the phase at time \(t=0\),
\(g_\mu = 0.01355342\) , the gyromagnetic ratio of muon,
\(g_e = 2.8024\) , the gyromagnetic ratio of electron,
and \(f_\text{cut} = 10^{32}\) (MHz).
(Source code, png, hires.png, pdf)
Properties (fitting parameters)¶
Name |
Default |
Description |
|---|---|---|
A0 |
0.2 |
Amplitude |
Field |
0.1 |
Magnetic Field (G) |
A |
0.2 |
Isotropic hyperfine coupling constant (MHz) |
Phi |
0.0 |
Phase (rad) |
References¶
[1] P. Percival, TRIUMF Summer Institute 2011.
[2] F.L. Pratt, Physica B 289-290, 710 (2000).
Categories: FitFunctions | Muon\MuonSpecific
Source¶
Python: LowTFMuonium.py